Phenomenological modeling of tumor diameter growth based on a mixed effects model

Abstract

Over the last few years, taking advantage of the linear kinetics of the tumor growth during the steady-state phase, tumor diameter-based rather than tumor volume-based models have been developed for the phenomenological modeling of tumor growth. In this study, we propose a new tumor diameter growth model characterizing early, late and steady-state treatment effects. Model parameters consist of growth rhythms, growth delays and time constants and are meaningful for biologists. Biological experiments provide in vivo longitudinal data. The latter are analyzed using a mixed effects model based on the new diameter growth function, to take into account inter-mouse variability and treatment factors. The relevance of the tumor growth mixed model is firstly assessed by analyzing the effects of three therapeutic strategies for cancer treatment (radiotherapy, concomitant radiochemotherapy and photodynamic therapy) administered on mice. Then, effects of the radiochemotherapy treatment duration are estimated within the mixed model. The results highlight the model suitability for analyzing therapeutic efficiency, comparing treatment responses and optimizing, when used in combination with optimal experiment design, anti-cancer treatment modalities.

Real-Time Monitoring of Photocytotoxicity in Nanoparticles-Based Photodynamic Therapy: A Model-Based Approach

“…This transformation is similar to the one previously proposed [32] to obtain a quasi-linear steady-state behaviour of the CI profile. To benefit from all the information contained in the TCI profiles, we propose to analyze them by a parametric model and to analyze the parameters as global characteristics of the complete in vitro response.…”

“…The CI variable was firstly transformed into a new modeling variable called transformed cell index (TCI) to obtain quasi-linear steady-state behaviour of the CI profile. Such a variable transformation was already applied to in vivo data for tumor response modeling [32]. We showed that an exponential-linear equation can describe all the measured TCI kinetics profiles.…”

A thermodynamic approach to the ‘mitosis/apoptosis’ ratio in cancer

“…These values are obtained by using some numerical approximations and data from the literature [1,[8][9][10][11][17][18][19][20][21][22][23][24][25][26][27][28][29]. Furthermore, the volume of a cell is approximated by a mean cell sphere with the diameter,…”

Tumor growth modeling based on cell and tumor lifespans

“…For instance, the tumor control probability (TCP) (Zaider and Minerbo, 2000;Dawson and Hillen, 2006;Gay and Niemierko, 2007) and the normal tissue complication probability (NTCP) (Lyman, 1985;Kallman et al, 1992) are used to characterize and evaluate the radiotherapy treatment planning. Their mathematical expressions can be derived from different stochastic models of the tumor response such as the linear quadratic model (Fowler, 1989;Zaider and Minerbo, 2000), cell populationdynamic models (Sachs et al, 2001), mixed-effects behavioral models (Bastogne, 2010) and cell cycle models (Kirkby et al, 2002). The main drawback of those mathematical representations is their inability to handle biological heterogeneity.…”